Vertical structure and physical processes of the Madden-Julian oscillation: exploring key model physics in climate simulations

Aimed at reducing deficiencies in representing the Madden-Julian oscillation (MJO) in general circulation models (GCMs), a global model evaluation project on vertical structure and physical processes of the MJO was coordinated. In this paper, results from the climate simulation component of this project are reported. It is shown that the MJO remains a great challenge in these latest generation GCMs. The systematic eastward propagation of the MJO is only well simulated in about one-fourth of the total participating models. The observed vertical westward tilt with altitude of the MJO is well simulated in good MJO models, but not in the poor ones. Damped Kelvin wave responses to the east of convection in the lower troposphere could be responsible for the missing MJO preconditioning process in these poor MJO models. Several process-oriented diagnostics were conducted to discriminate key processes for realistic MJO simulations. While large-scale rainfall partition and low-level mean zonal winds over the Indo-Pacific in a model are not found to be closely associated with its MJO skill, two metrics, including the low-level relative humidity difference between high and low rain events and seasonal mean gross moist stability, exhibit statistically significant correlations with the MJO performance. It is further indicated that increased cloud-radiative feedback tends to be associated with reduced amplitude of intraseasonal variability, which is incompatible with the radiative instability theory previously proposed for the MJO. Results in this study confirm that inclusion of air-sea interaction can lead to significant improvement in simulating the MJO.

Evaluation of the Met Office global forecast model using Geostationary Earth Radiation Budget (GERB) data

Simulations of the top-of-atmosphere radiative-energy budget from the Met Office global numerical weather-prediction model are evaluated using new data from the Geostationary Earth Radiation Budget (GERB) instrument on board the Meteosat-8 satellite. Systematic discrepancies between the model simulations and GERB measurements greater than 20 Wm-2 in outgoing long-wave radiation (OLR) and greater than 60 Wm-2 in reflected short-wave radiation (RSR) are identified over the period April-September 2006 using 12 UTC data. Convective cloud over equatorial Africa is spatially less organized and less reflective than in the GERB data. This bias depends strongly on convective-cloud cover, which is highly sensitive to changes in the model convective parametrization. Underestimates in model OLR over the Gulf of Guinea coincide with unrealistic southerly cloud outflow from convective centres to the north. Large overestimates in model RSR over the subtropical ocean, greater than 50 Wm-2 at 12 UTC, are explained by unrealistic radiative properties of low-level cloud relating to overestimation of cloud liquid water compared with independent satellite measurements. The results of this analysis contribute to the development and improvement of parametrizations in the global forecast model.

U.K. HiGEM: The New U.K. High-Resolution Global Environment Model���Model Description and Basic Evaluation

This article describes the development and evaluation of the U.K.���s new High-Resolution Global Environmental Model (HiGEM), which is based on the latest climate configuration of the Met Office Unified Model, known as the Hadley Centre Global Environmental Model, version 1 (HadGEM1). In HiGEM, the horizontal resolution has been increased to 0.83�� latitude �� 1.25�� longitude for the atmosphere, and 1/3�� �� 1/3�� globally for the ocean. Multidecadal integrations of HiGEM, and the lower-resolution HadGEM, are used to explore the impact of resolution on the fidelity of climate simulations. Generally, SST errors are reduced in HiGEM. Cold SST errors associated with the path of the North Atlantic drift improve, and warm SST errors are reduced in upwelling stratocumulus regions where the simulation of low-level cloud is better at higher resolution. The ocean model in HiGEM allows ocean eddies to be partially resolved, which dramatically improves the representation of sea surface height variability. In the Southern Ocean, most of the heat transports in HiGEM is achieved by resolved eddy motions, which replaces the parameterized eddy heat transport in the lower-resolution model. HiGEM is also able to more realistically simulate small-scale features in the wind stress curl around islands and oceanic SST fronts, which may have implications for oceanic upwelling and ocean biology. Higher resolution in both the atmosphere and the ocean allows coupling to occur on small spatial scales. In particular, the small-scale interaction recently seen in satellite imagery between the atmosphere and tropical instability waves in the tropical Pacific Ocean is realistically captured in HiGEM. Tropical instability waves play a role in improving the simulation of the mean state of the tropical Pacific, which has important implications for climate variability. In particular, all aspects of the simulation of ENSO (spatial patterns, the time scales at which ENSO occurs, and global teleconnections) are much improved in HiGEM.

Evaluation of a sequential global test of improved recovery following stroke as applied to the ICTUS trial of citicoline

The International Citicoline Trial in acUte Stroke is a sequential phase III study of the use of the drug citicoline in the treatment of acute ischaemic stroke, which was initiated in 2006 in 56 treatment centres. The primary objective of the trial is to demonstrate improved recovery of patients randomized to citicoline relative to those randomized to placebo after 12 weeks of follow-up. The primary analysis will take the form of a global test combining the dichotomized results of assessments on three well-established scales: the Barthel Index, the modified Rankin scale and the National Institutes of Health Stroke Scale. This approach was previously used in the analysis of the influential National Institute of Neurological Disorders and Stroke trial of recombinant tissue plasminogen activator in stroke. The purpose of this paper is to describe how this trial was designed, and in particular how the simultaneous objectives of taking into account three assessment scales, performing a series of interim analyses and conducting treatment allocation and adjusting the analyses to account for prognostic factors, including more than 50 treatment centres, were addressed. Copyright (C) 2008 John Wiley & Sons, Ltd.

Global retrieval of ATSR cloud parameters and evaluation (GRAPE): dataset assessment

The Along-Track Scanning Radiometers (ATSRs) provide a long time-series of measurements suitable for the retrieval of cloud properties. This work evaluates the freely-available Global Retrieval of ATSR Cloud Parameters and Evaluation (GRAPE) dataset (version 3) created from the ATSR-2 (1995��������2003) and Advanced ATSR (AATSR; 2002 onwards) records. Users are recommended to consider only retrievals flagged as high-quality, where there is a good consistency between the measurements and the retrieved state (corresponding to about 60% of converged retrievals over sea, and more than 80% over land). Cloud properties are found to be generally free of any significant spurious trends relating to satellite zenith angle. Estimates of the random error on retrieved cloud properties are suggested to be generally appropriate for optically-thick clouds, and up to a factor of two too small for optically-thin cases. The correspondence between ATSR-2 and AATSR cloud properties is high, but a relative calibration difference between the sensors of order 5��������10% at 660 nm and 870 nm limits the potential of the current version of the dataset for trend analysis. As ATSR-2 is thought to have the better absolute calibration, the discussion focusses on this portion of the record. Cloud-top heights from GRAPE compare well to ground-based data at four sites, particularly for shallow clouds. Clouds forming in boundary-layer inversions are typically around 1 km too high in GRAPE due to poorly-resolved inversions in the modelled temperature profiles used. Global cloud fields are compared to satellite products derived from the Moderate Resolution Imaging Spectroradiometer (MODIS), Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) measurements, and a climatology of liquid water content derived from satellite microwave radiometers. In all cases the main reasons for differences are linked to differing sensitivity to, and treatment of, multi-layer cloud systems. The correlation coefficient between GRAPE and the two MODIS products considered is generally high (greater than 0.7 for most cloud properties), except for liquid and ice cloud effective radius, which also show biases between the datasets. For liquid clouds, part of the difference is linked to choice of wavelengths used in the retrieval. Total cloud cover is slightly lower in GRAPE (0.64) than the CALIOP dataset (0.66). GRAPE underestimates liquid cloud water path relative to microwave radiometers by up to 100 g m��������2 near the Equator and overestimates by around 50 g m��������2 in the storm tracks. Finally, potential future improvements to the algorithm are outlined.

Mid-term evaluation of African Technology Policy Studies Network Phase VI Strategic Plan: for the period January 1, 2009 to December 31, 2010

The African Technology Policy Studies Network (ATPS) is a multidisciplinary network of researchers, private sector actors, policymakers and civil society. ATPS has the vision to become the leading international centre of excellence and reference in science, technology and innovation (STI) systems research, training and capacity building, communication and sensitization, knowledge brokerage, policy advocacy and outreach in Africa. It has a Regional Secretariat in Nairobi Kenya, and operates through national chapters in 29 countries (including 27 in Africa and two Chapters in the United Kingdom and USA for Africans in the Diaspora) with an expansion plan to cover the entire continent by 2015. The ATPS Phase VI Strategic Plan aims to improve the understanding and functioning of STI processes and systems to strengthen the learning capacity, social responses, and governance of STI for addressing Africa's development challenges, with a specific focus on the Millennium Development Goals (MDGs). A team of external evaluators carried out a midterm review to assess the effectiveness and efficiency of the implementation of the Strategic Plan for the period January 1, 2009 to December 31, 2010. The evaluation methodology involved multiple quantitative and qualitative methods to assess the qualitative and quantitative inputs (human resources, financial resources, time, etc.) into ATPS activities (both thematic and facilitative) and their tangible and intangible outputs, outcomes and impacts. Methods included a questionnaire survey of ATPS members and stakeholders, key informant interviews, and focus group discussions (FGDs) with members in six countries. Effectiveness of Programmes Under all six strategic goals, very good progress has been made towards planned outputs and outcomes. This is evidenced by key performance indicators (KPIs) generated from desk review, ratings from the survey respondents, and the themes that run through the FGDs. Institutional and Programme Cost Effectiveness Institutional Effectiveness: assessment of institutional effectiveness suggests that adequate management frameworks are in place and are being used effectively and transparently. Also technical and financial accounting mechanisms are being followed in accordance with grant agreements and with global good practice. This is evidenced by KPIs generated from desk review. Programme Cost Effectiveness: assessment of cost-effectiveness of execution of programmes shows that organisational structure is efficient, delivering high quality, relevant research at relatively low cost by international standards. The evidence includes KPIs from desk review: administrative costs to programme cost ratio has fallen steadily, to around 10%; average size of research grants is modest, without compromising quality. There is high level of pro bono input by ATPS members. ATPS Programmes Strategic Evaluation ATPS research and STI related activities are indeed unique and well aligned with STI issues and needs facing Africa and globally. The multi-disciplinary and trans-boundary nature of the research activities are creating a unique group of research scientists. The ATPS approach to research and STI issues is paving the way for the so called Third Generation University (3GU). Understanding this unique positioning, an increasing number of international multilateral agencies are seeking partnership with ATPS. ATPS is seeing an increasing level of funding commitments by Donor Partners. Recommendations for ATPS Continued Growth and Effectiveness On-going reform of ATPS administrative structure to continue The on-going reforms that have taken place within the Board, Regional Secretariat, and at the National Chapter coordination levels are welcomed. Such reform should continue until fully functional corporate governance policy and practices are fully established and implemented across the ATPS governance structures. This will further strengthen ATPS to achieve the vision of being the leading STI policy brokerage organization in Africa. Although training in corporate governance has been carried out for all sectors of ATPS leadership structure in recent time, there is some evidence that these systems have not yet been fully implemented effectively within all the governance structures of the organization, especially at the Board and National chapter levels. Future training should emphasize practical application with exercises relevant to ATPS leadership structure from the Board to the National Chapter levels. Training on Transformational Leadership - Leading a Change Though a subject of intense debate amongst economists and social scientists, it is generally agreed that cultural mindsets and attitudes could enhance and/or hinder organizational progress. ATPS���s vision demands transformational leadership skills amongst its leaders from the Board members to the National Chapter Coordinators. To lead such a change, ATPS leaders must understand and avoid personal and cultural mindsets and value systems that hinder change, while embracing those that enhance it. It requires deliberate assessment of cultural, behavioural patterns that could hinder progress and the willingness to be recast into cultural and personal habits that make for progress. Improvement of relationship amongst the Board, Secretariat, and National Chapters A large number of ATPS members and stakeholders feel they do not have effective communications and/or access to Board, National Chapter Coordinators and Regional Secretariat activities. Effort should be made to improve the implementation of ATPS communication strategy to improve on information flows amongst the ATPS management and the members. The results of the survey and the FGDs suggest that progress has been made during the past two years in this direction, but more could be done to ensure effective flow of pertinent information to members following ATPS communications channels. Strategies for Increased Funding for National Chapters There is a big gap between the fundraising skills of the Regional Secretariat and those of the National Coordinators. In some cases, funds successfully raised by the Secretariat and disbursed to national chapters were not followed up with timely progress and financial reports by some national chapters. Adequate training in relevant skills required for effective interactions with STI key policy players should be conducted regularly for National Chapter coordinators and ATPS members. The ongoing training in grant writing should continue and be made continent-wide if funding permits. Funding of National Chapters should be strategic such that capacity in a specific area of research is built which, with time, will not only lead to a strong research capacity in that area, but also strengthen academic programmes. For example, a strong climate change programme is emerging at University of Nigeria Nsukka (UNN), with strong collaborations with Universities from neighbouring States. Strategies to Increase National Government buy-in and support for STI Translating STI research outcomes into policies requires a great deal of emotional intelligence, skills which are often lacking in the first and second generation universities. In the epoch of the science-based or 2GUs, governments were content with universities carrying out scientific research and providing scientific education. Now they desire to see universities as incubators of new science- or technology-based commercial activities, whether by existing firms or start-ups. Hence, governments demand that universities take an active and leading role in the exploitation of their knowledge and they are willing to make funds available to support such activities. Thus, for universities to gain the attention of national leadership they must become centres of excellence and explicit instruments of economic development in the knowledge-based economy. The universities must do this while working collaboratively with government departments, parastatals, and institutions and dedicated research establishments. ATPS should anticipate these shifting changes and devise programmes to assist both government and universities to relate effectively. New administrative structures in member organizations to sustain and manage the emerging STI multidisciplinary teams Second Generation universities (2GUs) tend to focus on pure science and often do not regard the application of their know-how as their task. In contrast, Third Generation Universities (3GUs) objectively stimulate techno-starters ��� students or academics ��� to pursue the exploitation or commercialisation of the knowledge they generate. They view this as being equal in importance to the objectives of scientific research and education. Administratively, research in the 2GU era was mainly monodisciplinary and departments were structured along disciplines. The emerging interdisciplinary scientific teams with focus on specific research areas functionally work against the current mono-disciplinary faculty-based, administrative structure of 2GUs. For interdisciplinary teams, the current faculty system is an obstacle. There is a need for new organisational forms for university management that can create responsibilities for the task of know-how exploitation. ATPS must anticipate this and begin to strategize solutions for their member institutions to transition to 3Gus administrative structure, otherwise ATPS growth will plateau, and progress achieved so far may be stunted.

An urban parameterization for a global climate model. Part I: Formulation and evaluation for two cities

Urbanization, the expansion of built-up areas, is an important yet less-studied aspect of land use/land cover change in climate science. To date, most global climate models used to evaluate effects of land use/land cover change on climate do not include an urban parameterization. Here, the authors describe the formulation and evaluation of a parameterization of urban areas that is incorporated into the Community Land Model, the land surface component of the Community Climate System Model. The model is designed to be simple enough to be compatible with structural and computational constraints of a land surface model coupled to a global climate model yet complex enough to explore physically based processes known to be important in determining urban climatology. The city representation is based upon the ���urban canyon��� concept, which consists of roofs, sunlit and shaded walls, and canyon floor. The canyon floor is divided into pervious (e.g., residential lawns, parks) and impervious (e.g., roads, parking lots, sidewalks) fractions. Trapping of longwave radiation by canyon surfaces and solar radiation absorption and reflection is determined by accounting for multiple reflections. Separate energy balances and surface temperatures are determined for each canyon facet. A one-dimensional heat conduction equation is solved numerically for a 10-layer column to determine conduction fluxes into and out of canyon surfaces. Model performance is evaluated against measured fluxes and temperatures from two urban sites. Results indicate the model does a reasonable job of simulating the energy balance of cities.

Evaluation of high-resolution surface wind products at global and regional scales

High resolution surface wind fields covering the global ocean, estimated from remotely sensed wind data and ECMWF wind analyses, have been available since 2005 with a spatial resolution of 0.25 degrees in longitude and latitude, and a temporal resolution of 6h. Their quality is investigated through various comparisons with surface wind vectors from 190 buoys moored in various oceanic basins, from research vessels and from QuikSCAT scatterometer data taken during 2005-2006. The NCEP/NCAR and NCDC blended wind products are also considered. The comparisons performed during January-December 2005 show that speeds and directions compare well to in-situ observations, including from moored buoys and ships, as well as to the remotely sensed data. The root-mean-squared differences of the wind speed and direction for the new blended wind data are lower than 2m/s and 30 degrees, respectively. These values are similar to those estimated in the comparisons of hourly buoy measurements and QuickSCAT near real time retrievals. At global scale, it is found that the new products compare well with the wind speed and wind vector components observed by QuikSCAT. No significant dependencies on the QuikSCAT wind speed or on the oceanic region considered are evident.Evaluation of high-resolution surface wind products at global and regional scales

Intercomparison and evaluation of global aerosol microphysical properties among AeroCom models of a range of complexity

Many of the next generation of global climate models will include aerosol schemes which explicitly simulate the microphysical processes that determine the particle size distribution. These models enable aerosol optical properties and cloud condensation nuclei (CCN) concentrations to be determined by fundamental aerosol processes, which should lead to a more physically based simulation of aerosol direct and indirect radiative forcings. This study examines the global variation in particle size distribution simulated by 12 global aerosol microphysics models to quantify model diversity and to identify any common biases against observations. Evaluation against size distribution measurements from a new European network of aerosol supersites shows that the mean model agrees quite well with the observations at many sites on the annual mean, but there are some seasonal biases common to many sites. In particular, at many of these European sites, the accumulation mode number concentration is biased low during winter and Aitken mode concentrations tend to be overestimated in winter and underestimated in summer. At high northern latitudes, the models strongly underpredict Aitken and accumulation particle concentrations compared to the measurements, consistent with previous studies that have highlighted the poor performance of global aerosol models in the Arctic. In the marine boundary layer, the models capture the observed meridional variation in the size distribution, which is dominated by the Aitken mode at high latitudes, with an increasing concentration of accumulation particles with decreasing latitude. Considering vertical profiles, the models reproduce the observed peak in total particle concentrations in the upper troposphere due to new particle formation, although modelled peak concentrations tend to be biased high over Europe. Overall, the multi-model-mean data set simulates the global variation of the particle size distribution with a good degree of skill, suggesting that most of the individual global aerosol microphysics models are performing well, although the large model diversity indicates that some models are in poor agreement with the observations. Further work is required to better constrain size-resolved primary and secondary particle number sources, and an improved understanding of nucleation and growth (e.g. the role of nitrate and secondary organics) will improve the fidelity of simulated particle size distributions.

The AeroCom evaluation and intercomparison of organic aerosol in global models

This paper evaluates the current status of global modeling of the organic aerosol (OA) in the troposphere and analyzes the differences between models as well as between models and observations. Thirty-one global chemistry transport models (CTMs) and general circulation models (GCMs) have participated in this intercomparison, in the framework of AeroCom phase II. The simulation of OA varies greatly between models in terms of the magnitude of primary emissions, secondary OA (SOA) formation, the number of OA species used (2 to 62), the complexity of OA parameterizations (gas-particle partitioning, chemical aging, multiphase chemistry, aerosol microphysics), and the OA physical, chemical and optical properties. The diversity of the global OA simulation results has increased since earlier AeroCom experiments, mainly due to the increasing complexity of the SOA parameterization in models, and the implementation of new, highly uncertain, OA sources. Diversity of over one order of magnitude exists in the modeled vertical distribution of OA concentrations that deserves a dedicated future study. Furthermore, although the OA / OC ratio depends on OA sources and atmospheric processing, and is important for model evaluation against OA and OC observations, it is resolved only by a few global models. The median global primary OA (POA) source strength is 56 Tg a���1 (range 34���144 Tg a���1) and the median SOA source strength (natural and anthropogenic) is 19 Tg a���1 (range 13���121 Tg a���1). Among the models that take into account the semi-volatile SOA nature, the median source is calculated to be 51 Tg a���1 (range 16���121 Tg a���1), much larger than the median value of the models that calculate SOA in a more simplistic way (19 Tg a���1; range 13���20 Tg a���1, with one model at 37 Tg a���1). The median atmospheric burden of OA is 1.4 Tg (24 models in the range of 0.6���2.0 Tg and 4 between 2.0 and 3.8 Tg), with a median OA lifetime of 5.4 days (range 3.8���9.6 days). In models that reported both OA and sulfate burdens, the median value of the OA/sulfate burden ratio is calculated to be 0.77; 13 models calculate a ratio lower than 1, and 9 models higher than 1. For 26 models that reported OA deposition fluxes, the median wet removal is 70 Tg a���1 (range 28���209 Tg a���1), which is on average 85% of the total OA deposition. Fine aerosol organic carbon (OC) and OA observations from continuous monitoring networks and individual field campaigns have been used for model evaluation. At urban locations, the model���observation comparison indicates missing knowledge on anthropogenic OA sources, both strength and seasonality. The combined model���measurements analysis suggests the existence of increased OA levels during summer due to biogenic SOA formation over large areas of the USA that can be of the same order of magnitude as the POA, even at urban locations, and contribute to the measured urban seasonal pattern. Global models are able to simulate the high secondary character of OA observed in the atmosphere as a result of SOA formation and POA aging, although the amount of OA present in the atmosphere remains largely underestimated, with a mean normalized bias (MNB) equal to ���0.62 (���0.51) based on the comparison against OC (OA) urban data of all models at the surface, ���0.15 (+0.51) when compared with remote measurements, and ���0.30 for marine locations with OC data. The mean temporal correlations across all stations are low when compared with OC (OA) measurements: 0.47 (0.52) for urban stations, 0.39 (0.37) for remote stations, and 0.25 for marine stations with OC data. The combination of high (negative) MNB and higher correlation at urban stations when compared with the low MNB and lower correlation at remote sites suggests that knowledge about the processes that govern aerosol processing, transport and removal, on top of their sources, is important at the remote stations. There is no clear change in model skill with increasing model complexity with regard to OC or OA mass concentration. However, the complexity is needed in models in order to distinguish between anthropogenic and natural OA as needed for climate mitigation, and to calculate the impact of OA on climate accurately.

Decadal predictions with the HiGEM high resolution global coupled climate model: description and basic evaluation

This paper describes the development and basic evaluation of decadal predictions produced using the HiGEM coupled climate model. HiGEM is a higher resolution version of the HadGEM1 Met Office Unified Model. The horizontal resolution in HiGEM has been increased to 1.25��� �� 0.83��� in longitude and latitude for the atmosphere, and 1/3��� �� 1/3��� globally for the ocean. The HiGEM decadal predictions are initialised using an anomaly assimilation scheme that relaxes anomalies of ocean temperature and salinity to observed anomalies. 10 year hindcasts are produced for 10 start dates (1960, 1965,..., 2000, 2005). To determine the relative contributions to prediction skill from initial conditions and external forcing, the HiGEM decadal predictions are compared to uninitialised HiGEM transient experiments. The HiGEM decadal predictions have substantial skill for predictions of annual mean surface air temperature and 100 m upper ocean temperature. For lead times up to 10 years, anomaly correlations (ACC) over large areas of the North Atlantic Ocean, the Western Pacific Ocean and the Indian Ocean exceed values of 0.6. Initialisation of the HiGEM decadal predictions significantly increases skill over regions of the Atlantic Ocean,the Maritime Continent and regions of the subtropical North and South Pacific Ocean. In particular, HiGEM produces skillful predictions of the North Atlantic subpolar gyre for up to 4 years lead time (with ACC > 0.7), which are significantly larger than the uninitialised HiGEM transient experiments.

Evaluation of suitable spectral intervals for near-IR laboratory detection of water vapour continuum absorption

The water vapour continuum absorption is an important component of molecular absorption of radiation in atmosphere. However, uncertainty in knowledge of the value of the continuum absorption at present can achieve 100% in different spectral regions leading to an error in flux calculation up to 3-5 W/m2 global mean. This work uses line-by-line calculations to reveal the best spectral intervals for experimental verification of the CKD water vapour continuum models in the currently least studied near-infrared spectral region. Possible sources of errors in continuum retrieval taken into account in the simulation include the sensitivity of laboratory spectrometers and uncertainties in the spectral line parameters in HITRAN-2004 and Schwenke-Partridge database. It is shown that a number of micro-windows in near-IR can be used at present for laboratory detection of the water vapour continuum with estimated accuracy from 30 to 5%.

Efficient evaluation of highly oscillatory acoustic scattering surface integrals

We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost.