Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

Export of dissolved organic carbon from an upland peatland during storm events: implications for flux estimates

Most of the dissolved organic carbon (DOC) exported from catchments is transported during storm events. Accurate assessments of DOC fluxes are essential to understand long-term trends in the transport of DOC from terrestrial to aquatic systems, and also the loss of carbon from peatlands to determine changes in the source/sink status of peatland carbon stores. However, many long-term monitoring programmes collect water samples at a frequency (e.g. weekly/monthly) less than the time period of a typical storm event (typically <1–2 days). As widespread observations in catchments dominated by organo-mineral soils have shown that both concentration and flux of DOC increases during storm events, lower frequency monitoring could result in substantial underestimation of DOC flux as the most dynamic periods of transport are missed. However, our intensive monitoring study in a UK upland peatland catchment showed a contrasting response to these previous studies. Our results showed that (i) DOC concentrations decreased during autumn storm events and showed a poor relationship with flow during other seasons; and that (ii) this decrease in concentrations during autumn storms caused DOC flux estimates based on weekly monitoring data to be over-estimated, rather than under-estimated, because of over rather than under estimation of the flow-weighted mean concentration used in flux calculations. However, as DOC flux is ultimately controlled by discharge volume, and therefore rainfall, and the magnitude of change in discharge was greater than the magnitude of decline in concentrations, DOC flux increased during individual storm events. The implications for long-term DOC trends are therefore contradictory, as increased rainfall could increase flux but cause an overall decrease in DOC concentrations from peatland streams. Care needs to be taken when interpreting long-term trends in DOC flux rather than concentration; as flux is calculated from discharge estimates, and discharge is controlled by rainfall, DOC flux and rainfall/discharge will always be well correlated.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Contractor project estimates vs. consultant project estimates in Ghana

Ten projects constructed in Ghana between 2003 and 2010 are examined and analysed to ascertain the reliability of estimated costs provided for the projects. Cost estimates for five of the projects were calculated by consultants and cost estimates for the five remaining projects were calculated by contractors. Cost estimates prepared by contractors seemed to be closer to actual costs than estimates calculated by consultants. Projects estimated by consultants experienced an average cost overrun of 40% and time overrun of 62% whereas projects priced by contractors experienced an average cost overrun of 6% and time overrun of 41%. It seemed that contractors had a better understanding of the actual construction processes and a clearer expectation of the needs of the client hence an ability to calculate estimates that were closer to reality. Construction clients in Ghana should rely on contractors for more realistic cost estimates as estimates by consultants may be inaccurate. Where consultants are employed, an allowance of up 40% should be added to the estimated costs as a margin for inaccuracy.

The effect of surface heterogeneity on cloud absorption estimates

This study presents a systematic and quantitative analysis of the effect of inhomogeneous surface albedo on shortwave cloud absorption estimates. We used 3D radiative transfer modeling over a checkerboard surface albedo to calculate cloud absorption. We have found that accounting for surface heterogeneity enhances cloud absorption. However, the enhancement is not sufficient to explain the reported difference between measured and modeled cloud absorption.

The TAMORA algorithm: satellite rainfall estimates over West Africa using multi-spectral SEVIRI data

A multi-spectral rainfall estimation algorithm has been developed for the Sahel region of West Africa with the purpose of producing accumulated rainfall estimates for drought monitoring and food security. Radar data were used to calibrate multi-channel SEVIRI data from MSG, and a probability of rainfall at several different rain-rates was established for each combination of SEVIRI radiances. Radar calibrations from both Europe (the SatPrecip algorithm) and Niger (TAMORA algorithm) were used. 10 day estimates were accumulated from SatPrecip and TAMORA and compared with kriged gauge data and TAMSAT satellite rainfall estimates over West Africa. SatPrecip was found to produce large overestimates for the region, probably because of its non-local calibration. TAMORA was negatively biased for areas of West Africa with relatively high rainfall, but its skill was comparable to TAMSAT for the low-rainfall region climatologically similar to its calibration area around Niamey. These results confirm the high importance of local calibration for satellite-derived rainfall estimates. As TAMORA shows no improvement in skill over TAMSAT for dekadal estimates, the extra cloud-microphysical information provided by multi-spectral data may not be useful in determining rainfall accumulations at a ten day timescale. Work is ongoing to determine whether it shows improved accuracy at shorter timescales.

Emulating AOGCM results using simple climate models

Three simple climate models (SCMs) are calibrated using simulations from atmosphere ocean general circulation models (AOGCMs). In addition to using two conventional SCMs, results from a third simpler model developed specifically for this study are obtained. An easy to implement and comprehensive iterative procedure is applied that optimises the SCM emulation of global-mean surface temperature and total ocean heat content, and, if available in the SCM, of surface temperature over land, over the ocean and in both hemispheres, and of the global-mean ocean temperature profile. The method gives best-fit estimates as well as uncertainty intervals for the different SCM parameters. For the calibration, AOGCM simulations with two different types of forcing scenarios are used: pulse forcing simulations performed with 2 AOGCMs and gradually changing forcing simulations from 15 AOGCMs obtained within the framework of the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. The method is found to work well. For all possible combinations of SCMs and AOGCMs the emulation of AOGCM results could be improved. The obtained SCM parameters depend both on the AOGCM data and the type of forcing scenario. SCMs with a poor representation of the atmosphere thermal inertia are better able to emulate AOGCM results from gradually changing forcing than from pulse forcing simulations. Correct simultaneous emulation of both atmospheric temperatures and the ocean temperature profile by the SCMs strongly depends on the representation of the temperature gradient between the atmosphere and the mixed layer. Introducing climate sensitivities that are dependent on the forcing mechanism in the SCMs allows the emulation of AOGCM responses to carbon dioxide and solar insolation forcings equally well. Also, some SCM parameters are found to be very insensitive to the fitting, and the reduction of their uncertainty through the fitting procedure is only marginal, while other parameters change considerably. The very simple SCM is found to reproduce the AOGCM results as well as the other two comparably more sophisticated SCMs.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Report of the 2010 assessment of the scientific assessment panel: future ozone and its impact on surface UV

SCIENTIFIC SUMMARY Globally averaged total column ozone has declined over recent decades due to the release of ozone-depleting substances (ODSs) into the atmosphere. Now, as a result of the Montreal Protocol, ozone is expected to recover from the effects of ODSs as ODS abundances decline in the coming decades. However, a number of factors in addition to ODSs have led to and will continue to lead to changes in ozone. Discriminating between the causes of past and projected ozone changes is necessary, not only to identify the progress in ozone recovery from ODSs, but also to evaluate the effectiveness of climate and ozone protection policy options. Factors Affecting Future Ozone and Surface Ultraviolet Radiation • At least for the next few decades, the decline of ODSs is expected to be the major factor affecting the anticipated increase in global total column ozone. However, several factors other than ODS will affect the future evolution of ozone in the stratosphere. These include changes in (i) stratospheric circulation and temperature due to changes in long-lived greenhouse gas (GHG) abundances, (ii) stratospheric aerosol loading, and (iii) source gases of highly reactive stratospheric hydrogen and nitrogen compounds. Factors that amplify the effects of ODSs on ozone (e.g., stratospheric aerosols) will likely decline in importance as ODSs are gradually eliminated from the atmosphere. • Increases in GHG emissions can both positively and negatively affect ozone. Carbon dioxide (CO2)-induced stratospheric cooling elevates middle and upper stratospheric ozone and decreases the time taken for ozone to return to 1980 levels, while projected GHG-induced increases in tropical upwelling decrease ozone in the tropical lower stratosphere and increase ozone in the extratropics. Increases in nitrous oxide (N2O) and methane (CH4) concentrations also directly impact ozone chemistry but the effects are different in different regions. • The Brewer-Dobson circulation (BDC) is projected to strengthen over the 21st century and thereby affect ozone amounts. Climate models consistently predict an acceleration of the BDC or, more specifically, of the upwelling mass flux in the tropical lower stratosphere of around 2% per decade as a consequence of GHG abundance increases. A stronger BDC would decrease the abundance of tropical lower stratospheric ozone, increase poleward transport of ozone, and could reduce the atmospheric lifetimes of long-lived ODSs and other trace gases. While simulations showing faster ascent in the tropical lower stratosphere to date are a robust feature of chemistry-climate models (CCMs), this has not been confirmed by observations and the responsible mechanisms remain unclear. • Substantial ozone losses could occur if stratospheric aerosol loading were to increase in the next few decades, while halogen levels are high. Stratospheric aerosol increases may be caused by sulfur contained in volcanic plumes entering the stratosphere or from human activities. The latter might include attempts to geoengineer the climate system by enhancing the stratospheric aerosol layer. The ozone losses mostly result from enhanced heterogeneous chemistry on stratospheric aerosols. Enhanced aerosol heating within the stratosphere also leads to changes in temperature and circulation that affect ozone. • Surface ultraviolet (UV) levels will not be affected solely by ozone changes but also by the effects of climate change and by air quality change in the troposphere. These tropospheric effects include changes in clouds, tropospheric aerosols, surface reflectivity, and tropospheric sulfur dioxide (SO2) and nitrogen dioxide (NO2). The uncertainties in projections of these factors are large. Projected increases in tropospheric ozone are more certain and may lead to reductions in surface erythemal (“sunburning”) irradiance of up to 10% by 2100. Changes in clouds may lead to decreases or increases in surface erythemal irradiance of up to 15% depending on latitude. Expected Future Changes in Ozone Full ozone recovery from the effects of ODSs and return of ozone to historical levels are not synonymous. In this chapter a key target date is chosen to be 1980, in part to retain the connection to previous Ozone Assessments. Noting, however, that decreases in ozone may have occurred in some regions of the atmosphere prior to 1980, 1960 return dates are also reported. The projections reported on in this chapter are taken from a recent compilation of CCM simulations. The ozone projections, which also form the basis for the UV projections, are limited in their representativeness of possible futures since they mostly come from CCM simulations based on a single GHG emissions scenario (scenario A1B of Emissions Scenarios. A Special Report of Working Group III of the Intergovernmental Panel on Climate Change, Cambridge University Press, 2000) and a single ODS emissions scenario (adjusted A1 of the previous (2006) Ozone Assessment). Throughout this century, the vertical, latitudinal, and seasonal structure of the ozone distribution will be different from what it was in 1980. For this reason, ozone changes in different regions of the atmosphere are considered separately. • The projections of changes in ozone and surface clear-sky UV are broadly consistent with those reported on in the 2006 Assessment. • The capability of making projections and attribution of future ozone changes has been improved since the 2006 Assessment. Use of CCM simulations from an increased number of models extending through the entire period of ozone depletion and recovery from ODSs (1960–2100) as well as sensitivity simulations have allowed more robust projections of long-term changes in the stratosphere and of the relative contributions of ODSs and GHGs to those changes. • Global annually averaged total column ozone is projected to return to 1980 levels before the middle of the century and earlier than when stratospheric halogen loading returns to 1980 levels. CCM projections suggest that this early return is primarily a result of GHG-induced cooling of the upper stratosphere because the effects of circulation changes on tropical and extratropical ozone largely cancel. Global (90°S–90°N) annually averaged total column ozone will likely return to 1980 levels between 2025 and 2040, well before the return of stratospheric halogens to 1980 levels between 2045 and 2060. • Simulated changes in tropical total column ozone from 1960 to 2100 are generally small. The evolution of tropical total column ozone in models depends on the balance between upper stratospheric increases and lower stratospheric decreases. The upper stratospheric increases result from declining ODSs and a slowing of ozone destruction resulting from GHG-induced cooling. Ozone decreases in the lower stratosphere mainly result from an increase in tropical upwelling. From 1960 until around 2000, a general decline is simulated, followed by a gradual increase to values typical of 1980 by midcentury. Thereafter, although total column ozone amounts decline slightly again toward the end of the century, by 2080 they are no longer expected to be affected by ODSs. Confidence in tropical ozone projections is compromised by the fact that simulated decreases in column ozone to date are not supported by observations, suggesting that significant uncertainties remain. • Midlatitude total column ozone is simulated to evolve differently in the two hemispheres. Over northern midlatitudes, annually averaged total column ozone is projected to return to 1980 values between 2015 and 2030, while for southern midlatitudes the return to 1980 values is projected to occur between 2030 and 2040. The more rapid return to 1980 values in northern midlatitudes is linked to a more pronounced strengthening of the poleward transport of ozone due to the effects of increased GHG levels, and effects of Antarctic ozone depletion on southern midlatitudes. By 2100, midlatitude total column ozone is projected to be above 1980 values in both hemispheres. • October-mean Antarctic total column ozone is projected to return to 1980 levels after midcentury, later than in any other region, and yet earlier than when stratospheric halogen loading is projected to return to 1980 levels. The slightly earlier return of ozone to 1980 levels (2045–2060) results primarily from upper stratospheric cooling and resultant increases in ozone. The return of polar halogen loading to 1980 levels (2050–2070) in CCMs is earlier than in empirical models that exclude the effects of GHG-induced changes in circulation. Our confidence in the drivers of changes in Antarctic ozone is higher than for other regions because (i) ODSs exert a strong influence on Antarctic ozone, (ii) the effects of changes in GHG abundances are comparatively small, and (iii) projections of ODS emissions are more certain than those for GHGs. Small Antarctic ozone holes (areas of ozone <220 Dobson units, DU) could persist to the end of the 21st century. • March-mean Arctic total column ozone is projected to return to 1980 levels two to three decades before polar halogen loading returns to 1980 levels, and to exceed 1980 levels thereafter. While CCM simulations project a return to 1980 levels between 2020 and 2035, most models tend not to capture observed low temperatures and thus underestimate present-day Arctic ozone loss such that it is possible that this return date is biased early. Since the strengthening of the Brewer-Dobson circulation through the 21st century leads to increases in springtime Arctic column ozone, by 2100 Arctic ozone is projected to lie well above 1960 levels. Uncertainties in Projections • Conclusions dependent on future GHG levels are less certain than those dependent on future ODS levels since ODS emissions are controlled by the Montreal Protocol. For the six GHG scenarios considered by a few CCMs, the simulated differences in stratospheric column ozone over the second half of the 21st century are largest in the northern midlatitudes and the Arctic, with maximum differences of 20–40 DU between the six scenarios in 2100. • There remain sources of uncertainty in the CCM simulations. These include the use of prescribed ODS mixing ratios instead of emission fluxes as lower boundary conditions, the range of sea surface temperatures and sea ice concentrations, missing tropospheric chemistry, model parameterizations, and model climate sensitivity. • Geoengineering schemes for mitigating climate change by continuous injections of sulfur-containing compounds into the stratosphere, if implemented, would substantially affect stratospheric ozone, particularly in polar regions. Ozone losses observed following large volcanic eruptions support this prediction. However, sporadic volcanic eruptions provide limited analogs to the effects of continuous sulfur emissions. Preliminary model simulations reveal large uncertainties in assessing the effects of continuous sulfur injections. Expected Future Changes in Surface UV. While a number of factors, in addition to ozone, affect surface UV irradiance, the focus in this chapter is on the effects of changes in stratospheric ozone on surface UV. For this reason, clear-sky surface UV irradiance is calculated from ozone projections from CCMs. • Projected increases in midlatitude ozone abundances during the 21st century, in the absence of changes in other factors, in particular clouds, tropospheric aerosols, and air pollutants, will result in decreases in surface UV irradiance. Clear-sky erythemal irradiance is projected to return to 1980 levels on average in 2025 for the northern midlatitudes, and in 2035 for the southern midlatitudes, and to fall well below 1980 values by the second half of the century. However, actual changes in surface UV will be affected by a number of factors other than ozone. • In the absence of changes in other factors, changes in tropical surface UV will be small because changes in tropical total column ozone are projected to be small. By the middle of the 21st century, the model projections suggest surface UV to be slightly higher than in the 1960s, very close to values in 1980, and slightly lower than in 2000. The projected decrease in tropical total column ozone through the latter half of the century will likely result in clear-sky surface UV remaining above 1960 levels. Average UV irradiance is already high in the tropics due to naturally occurring low total ozone columns and high solar elevations. • The magnitude of UV changes in the polar regions is larger than elsewhere because ozone changes in polar regions are larger. For the next decades, surface clear-sky UV irradiance, particularly in the Antarctic, will continue to be higher than in 1980. Future increases in ozone and decreases in clear-sky UV will occur at slower rates than those associated with the ozone decreases and UV increases that occurred before 2000. In Antarctica, surface clear-sky UV is projected to return to 1980 levels between 2040 and 2060, while in the Arctic this is projected to occur between 2020 and 2030. By 2100, October surface clear-sky erythemal irradiance in Antarctica is likely to be between 5% below to 25% above 1960 levels, with considerable uncertainty. This is consistent with multi-model-mean October Antarctic total column ozone not returning to 1960 levels by 2100. In contrast, by 2100, surface clear-sky UV in the Arctic is projected to be 0–10% below 1960 levels.

Effects of beverage alcohol taxes and prices on drinking: a meta-analysis of 1003 estimates from 112 studies

Aims: We conducted a systematic review of studies examining relationships between measures of beverage alcohol tax or price levels and alcohol sales or self-reported drinking. A total of 112 studies of alcohol tax or price effects were found, containing 1003 estimates of the tax/price–consumption relationship. Design: Studies included analyses of alternative outcome measures, varying subgroups of the population, several statistical models, and using different units of analysis. Multiple estimates were coded from each study, along with numerous study characteristics. Using reported estimates, standard errors, t-ratios, sample sizes and other statistics, we calculated the partial correlation for the relationship between alcohol price or tax and sales or drinking measures for each major model or subgroup reported within each study. Random-effects models were used to combine studies for inverse variance weighted overall estimates of the magnitude and significance of the relationship between alcohol tax/price and drinking. Findings: Simple means of reported elasticities are -0.46 for beer, -0.69 for wine and -0.80 for spirits. Meta-analytical results document the highly significant relationships (P < 0.001) between alcohol tax or price measures and indices of sales or consumption of alcohol (aggregate-level r = -0.17 for beer, -0.30 for wine, -0.29 for spirits and -0.44 for total alcohol). Price/tax also affects heavy drinking significantly (mean reported elasticity = -0.28, individual-level r = -0.01, P < 0.01), but the magnitude of effect is smaller than effects on overall drinking. Conclusions: A large literature establishes that beverage alcohol prices and taxes are related inversely to drinking. Effects are large compared to other prevention policies and programs. Public policies that raise prices of alcohol are an effective means to reduce drinking.

Assessing the accuracy of CME speed and trajectory estimates from STEREO observations through a comparison of independent methods

We have estimated the speed and direction of propagation of a number of Coronal Mass Ejections (CMEs) using single-spacecraft data from the STEREO Heliospheric Imager (HI) wide-field cameras. In general, these values are in good agreement with those predicted by Thernisien, Vourlidas, and Howard in Solar Phys. 256, 111 -aEuro parts per thousand 130 (2009) using a forward modelling method to fit CMEs imaged by the STEREO COR2 coronagraphs. The directions of the CMEs predicted by both techniques are in good agreement despite the fact that many of the CMEs under study travel in directions that cause them to fade rapidly in the HI images. The velocities estimated from both techniques are in general agreement although there are some interesting differences that may provide evidence for the influence of the ambient solar wind on the speed of CMEs. The majority of CMEs with a velocity estimated to be below 400 km s(-1) in the COR2 field of view have higher estimated velocities in the HI field of view, while, conversely, those with COR2 velocities estimated to be above 400 km s(-1) have lower estimated HI velocities. We interpret this as evidence for the deceleration of fast CMEs and the acceleration of slower CMEs by interaction with the ambient solar wind beyond the COR2 field of view. We also show that the uncertainties in our derived parameters are influenced by the range of elongations over which each CME can be tracked. In order to reduce the uncertainty in the predicted arrival time of a CME at 1 Astronomical Unit (AU) to within six hours, the CME needs to be tracked out to at least 30 degrees elongation. This is in good agreement with predictions of the accuracy of our technique based on Monte Carlo simulations.

Drivers of fund performance: a panel data analysis

The principle aim of this research is to elucidate the factors driving the total rate of return of non-listed funds using a panel data analytical framework. In line with previous results, we find that core funds exhibit lower yet more stable returns than value-added and, in particular, opportunistic funds, both cross-sectionally and over time. After taking into account overall market exposure, as measured by weighted market returns, the excess returns of value-added and opportunity funds are likely to stem from: high leverage, high exposure to development, active asset management and investment in specialized property sectors. A random effects estimation of the panel data model largely confirms the findings obtained from the fixed effects model. Again, the country and sector property effect shows the strongest significance in explaining total returns. The stock market variable is negative which hints at switching effects between competing asset classes. For opportunity funds, on average, the returns attributable to gearing are three times higher than those for value added funds and over five times higher than for core funds. Overall, there is relatively strong evidence indicating that country and sector allocation, style, gearing and fund size combinations impact on the performance of unlisted real estate funds.