An historical perspective on forecast errors

Using annual observations on industrial production over the last three centuries, and on GDP over a 100-year period, we seek an historical perspective on the forecastability of these UK output measures. The series are dominated by strong upward trends, so we consider various specifications of this, including the local linear trend structural time-series model, which allows the level and slope of the trend to vary. Our results are not unduly sensitive to how the trend in the series is modelled: the average sizes of the forecast errors of all models, and the wide span of prediction intervals, attests to a great deal of uncertainty in the economic environment. It appears that, from an historical perspective, the postwar period has been relatively more forecastable.

A systematic approach to identify the sources of tropical SST errors in coupled models using the adjustment of initialised experiments

Understanding the sources of systematic errors in climate models is challenging because of coupled feedbacks and errors compensation. The developing seamless approach proposes that the identification and the correction of short term climate model errors have the potential to improve the modeled climate on longer time scales. In previous studies, initialised atmospheric simulations of a few days have been used to compare fast physics processes (convection, cloud processes) among models. The present study explores how initialised seasonal to decadal hindcasts (re-forecasts) relate transient week-to-month errors of the ocean and atmospheric components to the coupled model long-term pervasive SST errors. A protocol is designed to attribute the SST biases to the source processes. It includes five steps: (1) identify and describe biases in a coupled stabilized simulation, (2) determine the time scale of the advent of the bias and its propagation, (3) find the geographical origin of the bias, (4) evaluate the degree of coupling in the development of the bias, (5) find the field responsible for the bias. This strategy has been implemented with a set of experiments based on the initial adjustment of initialised simulations and exploring various degrees of coupling. In particular, hindcasts give the time scale of biases advent, regionally restored experiments show the geographical origin and ocean-only simulations isolate the field responsible for the bias and evaluate the degree of coupling in the bias development. This strategy is applied to four prominent SST biases of the IPSLCM5A-LR coupled model in the tropical Pacific, that are largely shared by other coupled models, including the Southeast Pacific warm bias and the equatorial cold tongue bias. Using the proposed protocol, we demonstrate that the East Pacific warm bias appears in a few months and is caused by a lack of upwelling due to too weak meridional coastal winds off Peru. The cold equatorial bias, which surprisingly takes 30 years to develop, is the result of an equatorward advection of midlatitude cold SST errors. Despite large development efforts, the current generation of coupled models shows only little improvement. The strategy proposed in this study is a further step to move from the current random ad hoc approach, to a bias-targeted, priority setting, systematic model development approach.

Quantifying errors due to frequency changes and target location uncertainty for radar refractivity retrievals

Radar refractivity retrievals can capture near-surface humidity changes, but noisy phase changes of the ground clutter returns limit the accuracy for both klystron- and magnetron-based systems. Observations with a C-band (5.6 cm) magnetron weather radar indicate that the correction for phase changes introduced by local oscillator frequency changes leads to refractivity errors no larger than 0.25 N units: equivalent to a relative humidity change of only 0.25% at 20°C. Requested stable local oscillator (STALO) frequency changes were accurate to 0.002 ppm based on laboratory measurements. More serious are the random phase change errors introduced when targets are not at the range-gate center and there are changes in the transmitter frequency (ΔfTx) or the refractivity (ΔN). Observations at C band with a 2-μs pulse show an additional 66° of phase change noise for a ΔfTx of 190 kHz (34 ppm); this allows the effect due to ΔN to be predicted. Even at S band with klystron transmitters, significant phase change noise should occur when a large ΔN develops relative to the reference period [e.g., ~55° when ΔN = 60 for the Next Generation Weather Radar (NEXRAD) radars]. At shorter wavelengths (e.g., C and X band) and with magnetron transmitters in particular, refractivity retrievals relative to an earlier reference period are even more difficult, and operational retrievals may be restricted to changes over shorter (e.g., hourly) periods of time. Target location errors can be reduced by using a shorter pulse or identified by a new technique making alternate measurements at two closely spaced frequencies, which could even be achieved with a dual–pulse repetition frequency (PRF) operation of a magnetron transmitter.

Compensation between resolved wave driving and parameterized orographic gravity wave driving of the Brewer–Dobson circulation and its response to climate change

Following recent findings, the interaction between resolved (Rossby) wave drag and parameterized orographic gravity wave drag (OGWD) is investigated, in terms of their driving of the Brewer–Dobson circulation (BDC), in a comprehensive climate model. To this end, the parameter that effectively determines the strength of OGWD in present-day and doubled CO2 simulations is varied. The authors focus on the Northern Hemisphere during winter when the largest response of the BDC to climate change is predicted to occur. It is found that increases in OGWD are to a remarkable degree compensated by a reduction in midlatitude resolved wave drag, thereby reducing the impact of changes in OGWD on the BDC. This compensation is also found for the response to climate change: changes in the OGWD contribution to the BDC response to climate change are compensated by opposite changes in the resolved wave drag contribution to the BDC response to climate change, thereby reducing the impact of changes in OGWD on the BDC response to climate change. By contrast, compensation does not occur at northern high latitudes, where resolved wave driving and the associated downwelling increase with increasing OGWD, both for the present-day climate and the response to climate change. These findings raise confidence in the credibility of climate model projections of the strengthened BDC.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Estimate of the cutoff errors in the Ewald summation for dipolar systems

Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The applicability of the estimates is tested and confirmed in several numerical examples. We demonstrate that these estimates can be used easily in determining the optimal parameters of the dipolar Ewald summation in the sense that they minimize the computation time for a predefined, user set, accuracy.

Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Increases in plasma sheet temperature with solar wind driving during substorm growth phases

During the substorm growth phase, magnetic reconnection extracts ~10^15 J from the solar wind through magnetic reconnection at the magnetopause, which is then stored in the magnetotail lobes. Plasma sheet pressure then increases to balance magnetic flux density increases in the lobes. We examine plasma sheet pressure, density and temperature during substorm growth phases using nine years of Cluster data (>316,000 data points). We show that plasma sheet pressure and temperature are higher during growth phases with higher solar wind driving whereas the density is approximately constant. We also show a weak correlation between plasma sheet temperature before onset and the minimum SuperMAG SML auroral index in the subsequent substorm. We discuss how energization of the plasma sheet before onset may result from thermodynamically adiabatic processes; how hotter plasma sheets may result in magnetotail instabilities and how this relates to the onset and size of the subsequent substorm expansion phase.

Finite sample weighting of recursive forecast errors

This paper proposes and tests a new framework for weighting recursive out-of-sample prediction errors according to their corresponding levels of in-sample estimation uncertainty. In essence, we show how to use the maximum possible amount of information from the sample in the evaluation of the prediction accuracy, by commencing the forecasts at the earliest opportunity and weighting the prediction errors. Via a Monte Carlo study, we demonstrate that the proposed framework selects the correct model from a set of candidate models considerably more often than the existing standard approach when only a small sample is available. We also show that the proposed weighting approaches result in tests of equal predictive accuracy that have much better sizes than the standard approach. An application to an exchange rate dataset highlights relevant differences in the results of tests of predictive accuracy based on the standard approach versus the framework proposed in this paper.

Mergers and acquisitions: driving the growth of MNEs

This paper examines the effects of internationalization (international diversification) and diversification across industries (product diversification) through mergers and acquisitions (M&As) on the firm’s risk-return profile. Drawing on the theoretical work of Vachani (1991) and Rugman and Verbeke’s (2004) metrics, we classify firms according to their degree of product diversification and global reach. These two dimensions at the firm-level are moderators for the performance–expansion relationship. To account for the endogeneity of market entry decisions, we develop a panel vector autoregression. We show that global and host-triad multinational enterprises (MNEs) benefit from cross-border M&As, which reinforces their geographic footprint. In contrast to all other types of firms, home-triad firms exhibit higher firm value without a change in risk when conducting cross-industry M&As. This effect, however, depends on the degree of product diversification. For home-triad firms with a small product range engaging in cross- industry transactions is a value-enhancing growth strategy.

Pragmatic solutions for syntactic problems: Understanding some L2 syntactic errors in terms of discourse-pragmatic deficits

Contemporary research in generative second language (L2) acquisition has attempted to address observable target-deviant aspects of L2 grammars within a UG-continuity framework (e.g. Lardiere 2000; Schwartz 2003; Sprouse 2004; Prévost & White 1999, 2000). With the aforementioned in mind, the independence of pragmatic and syntactic development, independently observed elsewhere (e.g. Grodzinsky & Reinhart 1993; Lust et al. 1986; Pacheco & Flynn 2005; Serratrice, Sorace & Paoli 2004), becomes particularly interesting. In what follows, I examine the resetting of the Null-Subject Parameter (NSP) for English learners of L2 Spanish. I argue that insensitivity to associated discoursepragmatic constraints on the discursive distribution of overt/null subjects accounts for what appear to be particular errors as a result of syntactic deficits. It is demonstrated that despite target-deviant performance, the majority must have native-like syntactic competence given their knowledge of the Overt Pronoun Constraint (Montalbetti 1984), a principle associated with the Spanish-type setting of the NSP.

Atmospheric and oceanic contributions to irreducible forecast uncertainty of Arctic surface climate

Uncertainty of Arctic seasonal to interannual predictions arising from model errors and initial state uncertainty has been widely discussed in the literature, whereas the irreducible forecast uncertainty (IFU) arising from the chaoticity of the climate system has received less attention. However, IFU provides important insights into the mechanisms through which predictability is lost, and hence can inform prioritization of model development and observations deployment. Here, we characterize how internal oceanic and surface atmospheric heat fluxes contribute to IFU of Arctic sea ice and upper ocean heat content in an Earth system model by analyzing a set of idealized ensemble prediction experiments. We find that atmospheric and oceanic heat flux are often equally important for driving unpredictable Arctic-wide changes in sea ice and surface water temperatures, and hence contribute equally to IFU. Atmospheric surface heat flux tends to dominate Arctic-wide changes for lead times of up to a year, whereas oceanic heat flux tends to dominate regionally and on interannual time scales. There is in general a strong negative covariance between surface heat flux and ocean vertical heat flux at depth, and anomalies of lateral ocean heat transport are wind-driven, which suggests that the unpredictable oceanic heat flux variability is mainly forced by the atmosphere. These results are qualitatively robust across different initial states, but substantial variations in the amplitude of IFU exist. We conclude that both atmospheric variability and the initial state of the upper ocean are key ingredients for predictions of Arctic surface climate on seasonal to interannual time scales.

Systematic and random errors between collocated satellite ice water path observations

There remains large disagreement between ice-water path (IWP) in observational data sets, largely because the sensors observe different parts of the ice particle size distribution. A detailed comparison of retrieved IWP from satellite observations in the Tropics (!30 " latitude) in 2007 was made using collocated measurements. The radio detection and ranging(radar)/light detection and ranging (lidar) (DARDAR) IWP data set, based on combined radar/lidar measurements, is used as a reference because it provides arguably the best estimate of the total column IWP. For each data set, usable IWP dynamic ranges are inferred from this comparison. IWP retrievals based on solar reflectance measurements, in the moderate resolution imaging spectroradiometer (MODIS), advanced very high resolution radiometer–based Climate Monitoring Satellite Applications Facility (CMSAF), and Pathfinder Atmospheres-Extended (PATMOS-x) datasets, were found to be correlated with DARDAR over a large IWP range (~20–7000 g m -2 ). The random errors of the collocated data sets have a close to lognormal distribution, and the combined random error of MODIS and DARDAR is less than a factor of 2, which also sets the upper limit for MODIS alone. In the same way, the upper limit for the random error of all considered data sets is determined. Data sets based on passive microwave measurements, microwave surface and precipitation products system (MSPPS), microwave integrated retrieval system (MiRS), and collocated microwave only (CMO), are largely correlated with DARDAR for IWP values larger than approximately 700 g m -2 . The combined uncertainty between these data sets and DARDAR in this range is slightly less MODIS-DARDAR, but the systematic bias is nearly an order of magnitude.

Processes driving intraseasonal displacements of the eastern edge of the warm pool: the contribution of westerly wind events

We investigate the processes responsible for the intraseasonal displacements of the eastern edge of the western Pacific warm pool (WPEE), which appear to play a role in the onset and development of El Niño events. We use 25 years of output from an ocean general circulation model experiment that is able to accurately capture the observed displacements of the WPEE, sea level anomalies, and upper ocean zonal currents at intraseasonal time scales in the western and central Pacific Ocean. Our results confirm that WPEE displacements driven by westerly wind events (WWEs) are largely controlled by zonal advection. This paper has also two novel findings: first, the zonal current anomalies responsible for the WPEE advection are driven primarily by local wind stress anomalies and not by intraseasonal wind-forced Kelvin waves as has been shown in most previous studies. Second, we find that intraseasonal WPEE fluctuations that are not related to WWEs are generally caused by intraseasonal variations in net heat flux, in contrast to interannual WPEE displacements that are largely driven by zonal advection. This study hence raises an interesting question: can surface heat flux-induced zonal WPEE motions contribute to El Niño–Southern Oscillation evolution, as WWEs have been shown to be able to do?

Concord Grape Juice, cognitive function and driving performance: a 12 week, placebo controlled, randomised, crossover trial in mothers of pre-teen children

Background: Daily consumption of Concord grape juice (CGJ) over three to four months has been shown to improve memory function in adults with mild cognitive impairment, and reduce blood pressure in hypertensive adults. These benefits are likely due to the high concentration of polyphenols in CGJ. Increased stress can impair cognitive function and elevate blood pressure. Thus we examined the potential beneficial effect of CGJ in individuals experiencing somewhat stressful demanding lifestyles. Objective: To examine the effects of twelve weeks’ daily consumption of CGJ on cognitive function, driving performance, and blood pressure in healthy, middle-aged working mothers. Design: Twenty five healthy mothers of pre-teen children, aged 40-50 years, who were employed for > 30 hours/week consumed 12oz (355ml) CGJ (containing 777mg total polyphenols) or an energy, taste and appearance matched placebo daily for twelve weeks according to a randomised, crossover design with a four week washout. Verbal and spatial memory, executive function, attention, blood pressure and mood were assessed at baseline, six weeks and twelve weeks. Immediately following the cognitive battery, a subsample of seventeen females completed a driving performance assessment in the University of Leeds Driving Simulator. The twenty five minute driving task required participants to match the speed and direction of a lead vehicle. Results: Significant improvements in immediate spatial memory and driving performance were observed following CGJ relative to placebo. There was evidence of an enduring effect of CGJ such that participants who received CGJ in arm 1 maintained better performance in the placebo arm. Conclusions: Cognitive benefits associated with chronic consumption of flavonoid-rich grape juice are not exclusive to adults with mild cognitive impairment. Moreover, these cognitive benefits are apparent in complex everyday tasks such as driving. Effects may persist beyond cessation of flavonoid consumption and future studies should carefully consider the length of washout within crossover designs.