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.

Negative blood oxygen level dependence in the rat: a model for investigating the role of suppression in neurovascular coupling

Modern neuroimaging techniques rely on neurovascular coupling to show regions of increased brain activation. However, little is known of the neurovascular coupling relationships that exist for inhibitory signals. To address this issue directly we developed a preparation to investigate the signal sources of one of these proposed inhibitory neurovascular signals, the negative blood oxygen level-dependent (BOLD) response (NBR), in rat somatosensory cortex. We found a reliable NBR measured in rat somatosensory cortex in response to unilateral electrical whisker stimulation, which was located in deeper cortical layers relative to the positive BOLD response. Separate optical measurements (two-dimensional optical imaging spectroscopy and laser Doppler flowmetry) revealed that the NBR was a result of decreased blood volume and flow and increased levels of deoxyhemoglobin. Neural activity in the NBR region, measured by multichannel electrodes, varied considerably as a function of cortical depth. There was a decrease in neuronal activity in deep cortical laminae. After cessation of whisker stimulation there was a large increase in neural activity above baseline. Both the decrease in neuronal activity and increase above baseline after stimulation cessation correlated well with the simultaneous measurement of blood flow suggesting that the NBR is related to decreases in neural activity in deep cortical layers. Interestingly, the magnitude of the neural decrease was largest in regions showing stimulus-evoked positive BOLD responses. Since a similar type of neural suppression in surround regions was associated with a negative BOLD signal, the increased levels of suppression in positive BOLD regions could importantly moderate the size of the observed BOLD response.

Ethylene and 1-methylcyclopropene differentially regulate gene expression during onion sprout suppression

Onion (Allium cepa) is regarded as a nonclimacteric vegetable. In onions, however, ethylene can suppress sprouting while the ethylene-binding inhibitor 1-methylcyclopropene (1-MCP) can also suppress sprout growth; yet, it is unknown how ethylene and 1-MCP elicit the same response. In this study, onions were treated with 10 mu L L(-1) ethylene or 1 mu L L(-1) 1-MCP individually or in combination for 24 h at 20 degrees C before or after curing (6 weeks) at 20 degrees C or 28 degrees C and then stored at 1 degrees C. Following curing, a subset of these same onions was stored separately under continuous air or ethylene (10 mu L L(-1)) at 1 degrees C. Onions treated with ethylene and 1-MCP in combination after curing for 24 h had reduced sprout growth as compared with the control 25 weeks after harvest. Sprout growth following storage beyond 25 weeks was only reduced through continuous ethylene treatment. This observation was supported by a higher proportion of down-regulated genes characterized as being involved in photosynthesis, measured using a newly developed onion microarray. Physiological and biochemical data suggested that ethylene was being perceived in the presence of 1-MCP, since sprout growth was reduced in onions treated with 1-MCP and ethylene applied in combination but not when applied individually. A cluster of probes representing transcripts up-regulated by 1-MCP alone but down-regulated by ethylene alone or in the presence of 1-MCP support this suggestion. Ethylene and 1-MCP both down-regulated a probe tentatively annotated as an ethylene receptor as well as ethylene-insensitive 3, suggesting that both treatments down-regulate the perception and signaling events of ethylene.

RNA interference suppression of genes in glycosyl transferase families 43 and 47 in wheat starchy endosperm causes large decreases in arabinoxylan content

The cell walls of wheat (Triticum aestivum) starchy endosperm are dominated by arabinoxylan (AX), accounting for 65% to 70% of the polysaccharide content. Genes within two glycosyl transferase (GT) families, GT43 (IRREGULAR XYLEM9 [IRX9] and IRX14) and GT47 (IRX10), have previously been shown to be involved in the synthesis of the xylan backbone in Arabidopsis, and close homologs of these have been implicated in the synthesis of xylan in other species. Here, homologs of IRX10 TaGT47_2 and IRX9 TaGT43_2, which are highly expressed in wheat starchy endosperm cells, were suppressed by RNA interference (RNAi) constructs driven by a starchy endosperm-specific promoter. The total amount of AX was decreased by 40% to 50% and the degree of arabinosylation was increased by 25% to 30% in transgenic lines carrying either of the transgenes. The cell walls of starchy endosperm in sections of grain from TaGT43_2 and TaGT47_2 RNAi transgenics showed decreased immunolabeling for xylan and arabinoxylan epitopes and approximately 50% decreased cell wall thickness compared with controls. The proportion of AX that was water soluble was not significantly affected, but average AX polymer chain length was decreased in both TaGT43_2 and TaGT47_2 RNAi transgenics. However, the long AX chains seen in controls were absent in TaGT43_2 RNAi transgenics but still present in TaGT47_2 RNAi transgenics. The results support an emerging picture of IRX9-like and IRX10-like proteins acting as key components in the xylan synthesis machinery in both dicots and grasses. Since AX is the main component of dietary fiber in wheat foods, the TaGT43_2 and TaGT47_2 genes are of major importance to human nutrition.

Suppression of gliadins results in altered protein body morphology in wheat

Wheat gluten proteins, gliadins and glutenins, are of great importance in determining the unique biomechanical properties of wheat. Studies have therefore been carried out to determine their pathways and mechanisms of synthesis, folding, and deposition in protein bodies. In the present work, a set of transgenic wheat lines has been studied with strongly suppressed levels of γ-gliadins and/or all groups of gliadins, using light and fluorescence microscopy combined with immunodetection using specific antibodies for γ-gliadins and HMW glutenin subunits. These lines represent a unique material to study the formation and fusion of protein bodies in developing seeds of wheat. Higher amounts of HMW subunits were present in most of the transgenic lines but only the lines with suppression of all gliadins showed differences in the formation and fusion of the protein bodies. Large rounded protein bodies were found in the wild-type lines and the transgenic lines with reduced levels of γ-gliadins, while the lines with all gliadins down-regulated had protein bodies of irregular shape and irregular formation. The size and number of inclusions, which have been reported to contain triticins, were also higher in the protein bodies in the lines with all the gliadins down-regulated. Changes in the protein composition and PB morphology reported in the transgenic lines with all gliadins down-regulated did not result in marked changes in the total protein content or instability of the different fractions.

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.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

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.

Memory suppression can help people “unlearn” behavioral responses—but only for nonemotional memories

When encountering reminders of memories that we prefer not to think about, we often try to exclude those memories from awareness. Past studies have revealed that such suppression attempts can reduce the subsequent recollection of unwanted memories. In the present study, we examined whether the inhibitory effects extend even to associated behavioral responses. Participants learned cue–target pairs for emotional and nonemotional targets and were additionally trained in behavioral responses for each cue. Afterward, they were shown the cues and instructed either to think or to avoid thinking about the targets without performing any behaviors. In a final test phase, behavioral performance was tested for all of the cues. When the targets were neutral, participants’ attempts to avoid retrieval reduced accuracy and increased reaction times in generating behavioral responses associated with cues. By contrast, behavioral performance was not affected by suppression attempts when the targets were emotional. These results indicate that controlling unwanted recollection is powerful enough to inhibit associated behavioral responses—but only for nonemotional memories.

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.

Emotion regulation meets emotional attention: the influence of emotion suppression on emotional attention depends on the nature of the distracters

Recent evidence has suggested a crucial role of people’s current goals in attention to emotional information. This asks for research investigating how and what kinds of goals shape emotional attention. The present study investigated how the goal to suppress a negative emotional state influences attention to emotion-congruent events. After inducing disgust, we instructed participants to suppress all feelings of disgust during a subsequent dot probe task. Attention to disgusting images was modulated by the sort of distracter that was presented in parallel with disgusting imagery. When disgusting images were presented together with neutral images, emotion suppression was accompanied by a tendency to attend to disgusting images. However, when disgusting images were shown with positive images that allow coping with disgust (i.e., images representing cleanliness), attention tended away from disgusting images and toward images representing cleanliness. These findings show that emotion suppression influences the allocation of attention but that the successful avoidance of emotion-congruent events depends on the availability of effective distracters.