Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones. The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.

Wave activity in the tropical tropopause layer in seven reanalysis and four chemistry climate model data sets

Sub-seasonal variability including equatorial waves significantly influence the dehydration and transport processes in the tropical tropopause layer (TTL). This study investigates the wave activity in the TTL in 7 reanalysis data sets (RAs; NCEP1, NCEP2, ERA40, ERA-Interim, JRA25, MERRA, and CFSR) and 4 chemistry climate models (CCMs; CCSRNIES, CMAM, MRI, and WACCM) using the zonal wave number-frequency spectral analysis method with equatorially symmetric-antisymmetric decomposition. Analyses are made for temperature and horizontal winds at 100 hPa in the RAs and CCMs and for outgoing longwave radiation (OLR), which is a proxy for convective activity that generates tropopause-level disturbances, in satellite data and the CCMs. Particular focus is placed on equatorial Kelvin waves, mixed Rossby-gravity (MRG) waves, and the Madden-Julian Oscillation (MJO). The wave activity is defined as the variance, i.e., the power spectral density integrated in a particular zonal wave number-frequency region. It is found that the TTL wave activities show significant difference among the RAs, ranging from ∼0.7 (for NCEP1 and NCEP2) to ∼1.4 (for ERA-Interim, MERRA, and CFSR) with respect to the averages from the RAs. The TTL activities in the CCMs lie generally within the range of those in the RAs, with a few exceptions. However, the spectral features in OLR for all the CCMs are very different from those in the observations, and the OLR wave activities are too low for CCSRNIES, CMAM, and MRI. It is concluded that the broad range of wave activity found in the different RAs decreases our confidence in their validity and in particular their value for validation of CCM performance in the TTL, thereby limiting our quantitative understanding of the dehydration and transport processes in the TTL.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (~ 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.

On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Causal relationship between obesity and vitamin D status: bi-directional mendelian randomization analysis of multiple cohorts

BACKGROUND: Obesity is associated with vitamin D deficiency, and both are areas of active public health concern. We explored the causality and direction of the relationship between body mass index (BMI) and 25-hydroxyvitamin D [25(OH)D] using genetic markers as instrumental variables (IVs) in bi-directional Mendelian randomization (MR) analysis. METHODS AND FINDINGS: We used information from 21 adult cohorts (up to 42,024 participants) with 12 BMI-related SNPs (combined in an allelic score) to produce an instrument for BMI and four SNPs associated with 25(OH)D (combined in two allelic scores, separately for genes encoding its synthesis or metabolism) as an instrument for vitamin D. Regression estimates for the IVs (allele scores) were generated within-study and pooled by meta-analysis to generate summary effects. Associations between vitamin D scores and BMI were confirmed in the Genetic Investigation of Anthropometric Traits (GIANT) consortium (n = 123,864). Each 1 kg/m(2) higher BMI was associated with 1.15% lower 25(OH)D (p = 6.52×10⁻²⁷). The BMI allele score was associated both with BMI (p = 6.30×10⁻⁶²) and 25(OH)D (-0.06% [95% CI -0.10 to -0.02], p = 0.004) in the cohorts that underwent meta-analysis. The two vitamin D allele scores were strongly associated with 25(OH)D (p≤8.07×10⁻⁵⁷ for both scores) but not with BMI (synthesis score, p = 0.88; metabolism score, p = 0.08) in the meta-analysis. A 10% higher genetically instrumented BMI was associated with 4.2% lower 25(OH)D concentrations (IV ratio: -4.2 [95% CI -7.1 to -1.3], p = 0.005). No association was seen for genetically instrumented 25(OH)D with BMI, a finding that was confirmed using data from the GIANT consortium (p≥0.57 for both vitamin D scores). CONCLUSIONS: On the basis of a bi-directional genetic approach that limits confounding, our study suggests that a higher BMI leads to lower 25(OH)D, while any effects of lower 25(OH)D increasing BMI are likely to be small. Population level interventions to reduce BMI are expected to decrease the prevalence of vitamin D deficiency.

Exploring writing in products in students with language impairments and autism spectrum disorders

Oral language skills scaffold written text production; students with oral language difficulties often experience writing problems. The current study examines the ways in which oral language problems experienced by students with language impairment (LI) and students with autism spectrum disorders (ASD) impact on their production of written text. One hundred and fifty seven participants (Mage = 10;2) with LI or ASD completed standardized measures of oral language, transcription, working memory, and nonverbal ability and produced a written narrative text assessed for productivity, grammatical accuracy, and quality. Measures of transcription, productivity, and grammatical accuracy, but not text quality, were poorer for students with LI. Transcription skills accounted for the majority of variance in the writing of the LI cohort. For the ASD cohort, handwriting, oral language and autism symptomatology were significant predictors. When students with ASD also experienced language problems, their performance was equivalent to that observed in the LI cohort.

Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances

Using 1D Vlasov drift-kinetic computer simulations, it is shown that electron trapping in long period standing shear Alfven waves (SAWs) provides an efficient energy sink for wave energy that is much more effective than Landau damping. It is also suggested that the plasma environment of low altitude auroral-zone geomagnetic field lines is more suited to electron acceleration by inertial or kinetic scale Alfven waves. This is due to the self-consistent response of the electron distribution function to SAWs, which must accommodate the low altitude large-scale current system in standing waves. We characterize these effects in terms of the relative magnitude of the wave phase and electron thermal velocities. While particle trapping is shown to be significant across a wide range of plasma temperatures and wave frequencies, we find that electron beam formation in long period waves is more effective in relatively cold plasma.

Systematic model forecast error in Rossby wave structure

Diabatic processes can alter Rossby wave structure; consequently errors arising from model processes propagate downstream. However, the chaotic spread of forecasts from initial condition uncertainty renders it difficult to trace back from root mean square forecast errors to model errors. Here diagnostics unaffected by phase errors are used, enabling investigation of systematic errors in Rossby waves in winter-season forecasts from three operational centers. Tropopause sharpness adjacent to ridges decreases with forecast lead time. It depends strongly on model resolution, even though models are examined on a common grid. Rossby wave amplitude reduces with lead time up to about five days, consistent with under-representation of diabatic modification and transport of air from the lower troposphere into upper-tropospheric ridges, and with too weak humidity gradients across the tropopause. However, amplitude also decreases when resolution is decreased. Further work is necessary to isolate the contribution from errors in the representation of diabatic processes.

Abnormal functional activation and maturation of fronto-striato-temporal and cerebellar regions during sustained attention in autism spectrum disorder

Objective Sustained attention problems are common in people with autism spectrum disorder (ASD) and may have significant implications for the diagnosis and management of ASD and associated comorbidities. Furthermore, ASD has been associated with atypical structural brain development. The authors used functional MRI to investigate the functional brain maturation of attention between childhood and adulthood in people with ASD. Method Using a parametrically modulated sustained attention/vigilance task, the authors examined brain activation and its linear correlation with age between childhood and adulthood in 46 healthy male adolescents and adults (ages 11–35 years) with ASD and 44 age- and IQ-matched typically developing comparison subjects. Results Relative to the comparison group, the ASD group had significantly poorer task performance and significantly lower activation in inferior prefrontal cortical, medial prefrontal cortical, striato-thalamic, and lateral cerebellar regions. A conjunction analysis of this analysis with group differences in brain-age correlations showed that the comparison group, but not the ASD group, had significantly progressively increased activation with age in these regions between childhood and adulthood, suggesting abnormal functional brain maturation in ASD. Several regions that showed both abnormal activation and functional maturation were associated with poorer task performance and clinical measures of ASD and inattention. Conclusions The results provide first evidence that abnormalities in sustained attention networks in individuals with ASD are associated with underlying abnormalities in the functional brain maturation of these networks between late childhood and adulthood.

The physics of orographic gravity wave drag

The drag and momentum fluxes produced by gravity waves generated in flow over orography are reviewed, focusing on adiabatic conditions without phase transitions or radiation effects, and steady mean incoming flow. The orographic gravity wave drag is first introduced in its simplest possible form, for inviscid, linearized, non-rotating flow with the Boussinesq and hydrostatic approximations, and constant wind and static stability. Subsequently, the contributions made by previous authors (primarily using theory and numerical simulations) to elucidate how the drag is affected by additional physical processes are surveyed. These include the effect of orography anisotropy, vertical wind shear, total and partial critical levels, vertical wave reflection and resonance, non-hydrostatic effects and trapped lee waves, rotation and nonlinearity. Frictional and boundary layer effects are also briefly mentioned. A better understanding of all of these aspects is important for guiding the improvement of drag parametrization schemes.

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.

The effect of chosen extraterrestrial solar spectrum on clear-sky atmospheric absorption and heating rates in the near infrared

The extraterrestrial solar spectrum (ESS) is an important component in near infrared (near-IR) radiative transfer calculations. However, the impact of a particular choice of the ESS in these regions has been given very little attention. A line-by-line (LBL) transfer model has been used to calculate the absorbed solar irradiance and solar heating rates in the near-IR from 2000-10000 cm−1(1-5 μm) using different ESS. For overhead sun conditions in a mid-latitude summer atmosphere, the absorbed irradiances could differ by up to about 11 Wm−2 (8.2%) while the tropospheric and stratospheric heating rates could differ by up to about 0.13 K day−1 (8.1%) and 0.19 K day−1 (7.6%). The spectral shape of the ESS also has a small but non-negligible impact on these factors in the near-IR.

Emotional and behavioural problems in children with language impairments and children with autism spectrum disorders

Background: Although it is well-established that children with language impairment (LI) and children with autism spectrum disorders (ASD) both show elevated levels of emotional and behavioural problems, the level and types of difficulties across the two groups have not previously been directly compared. Aims: To compare levels of emotional and behavioural problems in children with LI and children with ASD recruited from the same mainstream schools. Methods & Procedures: We measured teacher-reported emotional and behavioural problems using the Strengths and Difficulties Questionnaire (SDQ) in a sample of 5-to-13-year old children with LI (N=62) and children with ASD (N=42) attending mainstream school but with identified special educational needs. Outcomes & Results: Both groups showed similarly elevated levels of emotional, conduct and hyperactivity problems. The only differences between the LI and ASD groups were on subscales assessing peer problems (which were higher in the ASD group) and prosocial behaviours (which were higher in the LI group). Overall, there were few associations between emotional and behavioural problems and child characteristics, reflecting the pervasive nature of these difficulties in children with LI and children with ASD, although levels of problems were higher in children with ASD with lower language ability. However, in the ASD group only, a measure of family social economic status was associated with language ability and attenuated the association between language ability and emotional and behavioural problems. Conclusions & Implications: Children with LI and children with ASD in mainstream school show similarly elevated levels of emotional and behavioural problems, which require monitoring and may benefit from intervention. Further work is required to identify the child, family and situational factors that place children with LI and children with ASD at risk of emotional and behavioural problems, and whether these differ between the two groups. This work can then guide the application of evidence-based interventions to these children.

Translation and usability of autism screening and diagnostic tools for autism spectrum conditions in India

There is a critical need for screening and diagnostic tools (SDT) for autism spectrum conditions (ASC) in regional languages in South Asia. To address this, we translated four widely used SDT (Social Communication Disorder Checklist, Autism Spectrum Quotient, Social Communication Questionnaire, and Autism Diagnostic Observation Schedule) into Bengali and Hindi, two main regional languages (∼ 360 million speakers), and tested their usability in children with and without ASC. We found a significant difference in scores between children with ASC (n = 45 in Bengali, n = 40 in Hindi) and typically developing children (n = 43 in Bengali, n = 42 in Hindi) on all SDTs. These results demonstrate that these SDTs are usable in South Asia, and constitute an important resource for epidemiology research and clinical diagnosis in the region.